지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회지 대한수학회지 제58권 제5호
- 발행연도
- 2021.9
- 수록면
- 1,181 - 1,209 (29page)
- DOI
- 10.4134/JKMS.j200497
이용수
초록· 키워드
오류제보하기
In the present paper, we are concerned with the existence of ground state sign-changing solutions for the following Schr\"{o}dinger-Poisson-Kirchhoff system $$\left\{ \aligned &-(1\!+\!b\int_{\mathbb R^3}|\nabla u|^{2}dx)\triangle u \!+\! V(x)u \!+\! k(x) \phi u\!=\! \lambda f(x)u \!+\! |u|^{4}u, &\hbox{in}\ \ \mathbb{R}^{3},\\ & -\triangle \phi \!=\! k(x) u^{2}, & \hbox{in}\ \ \mathbb{R}^{3},\endaligned\right.$$ where $b>0$, $V(x)$, $k(x)$ and $f(x)$ are positive continuous smooth functions; $0<\lambda<\lambda_{1}$ and $\lambda_{1}$ is the first eigenvalue of the problem $-\triangle u + V(x)u = \lambda f(x)u$ in $H$. With the help of the constraint variational method, we obtain that the Schr\"{o}dinger-Poisson-Kirchhoff type system possesses at least one ground state sign-changing solution for all $b>0$ and $0<\lambda<\lambda_{1}$. Moreover, we prove that its energy is strictly larger than twice that of the ground state solutions of Nehari type.
목차
등록된 정보가 없습니다.
참고문헌 (26)
참고문헌 신청
ANTONIO AMBROSETTI / 2012 / MULTIPLE BOUND STATES FOR THE SCHRÖDINGER–POISSON PROBLEM / Communications in Contemporary Mathematics 10(03):391~404
Thomas Bartsch / 2005 / Partial symmetry of least energy nodal solutions to some variational problems / Journal d'Analyse Mathématique 96(1):1~18
Vieri Benci / 1998 / An eigenvalue problem for the Schrödinger-Maxwell equations / Topological Methods in Nonlinear Analysis 11(2):283
Haïm Brezis / 1983 / Positive solutions of nonlinear elliptic equations involving critical sobolev exponents / Communications on Pure and Applied Mathematics 36(4):437~477
K.J. Brown / 2003 / The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function / Journal of Differential Equations 193(2):481~499
Thomas Bartsch / 2005 / Partial symmetry of least energy nodal solutions to some variational problems / Journal d'Analyse Mathématique 96(1):1~18
Vieri Benci / 1998 / An eigenvalue problem for the Schrödinger-Maxwell equations / Topological Methods in Nonlinear Analysis 11(2):283
Haïm Brezis / 1983 / Positive solutions of nonlinear elliptic equations involving critical sobolev exponents / Communications on Pure and Applied Mathematics 36(4):437~477
K.J. Brown / 2003 / The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function / Journal of Differential Equations 193(2):481~499
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
Ground state sign-changing solutions for nonlinear Schr\"{o}dinger-Poisson system with indefinite potentials
대한수학회논문집
2022 .10
-
The fractional Schr\"{o}dinger-Poisson systems with infinitely many solutions
대한수학회지
2020 .01
-
Existence and multiplicity of solutions for nonlinear Schr\"{o}dinger-Kirchhoff-type equations
대한수학회지
2016 .01
-
ODEs related with some nonlocal Schr\"{o}dinger equations and its applications
대한수학회논문집
2019 .01
-
Existence and multiplicity of solutions for Kirchhoff-Schr\"{o}dinger-Poisson system with concave and convex nonlinearities
대한수학회지
2020 .01
-
EXISTENCE AND CONCENTRATION RESULTS FOR KIRCHHOFF-TYPE SCHR¨O DINGER SYSTEMS WITH STEEP POTENTIAL WELL
대한수학회보
2015 .01
-
Positive solution and ground state solution for a Kirchhoff type equation with critical growth
대한수학회보
2022 .07
-
Hardy type estimates for Riesz transforms associated with Schr\"{o}dinger operators on the Heisenberg group
대한수학회지
2022 .03
-
Multiple solutions for a class of quasilinear Schr\"{o}dinger system in $\mathbb{R}^N$
대한수학회보
2016 .01
-
Multiplicity results for nonlinear Schr\"{o}dinger-Poisson systems with subcritical or critical growth
대한수학회지
2016 .01
-
Theta sums of higher index
대한수학회보
2016 .01
-
Quasilinear Schr\"{o}dinger equations for the Heisenberg ferromagnetic spin chain
대한수학회보
2024 .03
-
Bifurcation problem for a class of quasilinear fractional Schr\"{o}dinger equations
대한수학회지
2020 .01
-
Exponential Decay for the Solution of the Viscoelastic Kirchhoff Type Equation with Memory Condition at the Boundary
East Asian Mathematical Journal
2018 .01
-
Estimates for Schr\"{o}dinger maximal operators along curve with complex time
대한수학회지
2020 .01
-
On solvability of a class of degenerate Kirchhoff equations with logarithmic nonlinearity
대한수학회지
2023 .05
-
EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR A SCHRO ̈DINGER-TYPE SINGULAR FALLING ZERO PROBLEM
East Asian Mathematical Journal
2023 .05
-
Regularity of the generalized Poisson operator
대한수학회지
2022 .01
-
Numerical solutions for one and two dimensional nonlinear problems related to dispersion managed solitons
대한수학회지
2021 .01
-
Existence of weak solutions to a class of Schr\"{o}dinger type equations involving the fractional $p$-Laplacian in $\mathbb R^{N}$
대한수학회지
2019 .01
이 논문의 저자 정보
최근 본 자료
댓글(0)
0